@article { ,
title = {Near optimal spectral gaps for hyperbolic surfaces},
abstract = {We prove that if X is a finite area non-compact hyperbolic surface, then for any ϵ > 0, with probability tending to one as n → ∞, a uniformly random degree n Riemannian cover of X has no eigenvalues of the Laplacian in [0, 1 4 − ϵ) other than those of X, and with the same multiplicities. As a result, using a compactification procedure due to Buser, Burger, and Dodziuk, we settle in the affirmative the question of whether there exists a sequence of closed hyperbolic surfaces with genera tending to infinity and first non-zero eigenvalue of the Laplacian tending to 1 4 .},
doi = {10.4007/annals.2023.198.2.6},
issn = {0003-486X},
issue = {2},
journal = {Annals of Mathematics},
note = {EPrint Processing Status: Full text deposited in DRO, closed access},
pages = {791-824},
publicationstatus = {Published},
publisher = {Department of Mathematics},
url = {https://durham-repository.worktribe.com/output/1176898},
volume = {198},
year = {2024},
author = {Hide, Will and Magee, Michael}
}